As a second data point, here's the comparison from one of our 4-year state universities. Compared are math major with teaching certification (MM), and secondary ed major with math option (SE).
2144 (SE only, but a prereq for 2153) Calculus I
2153 (both) Calculus II
2163 (both) Calculus III
2233 (both) Differential Equations
3013 (both) Linear Algebra
3613 (both)Introduction to Modern Algebra
4023 (MM only - can count as an elective for SE)Introduction to Modern Analysis
4033 (both) History of Mathematics
4403 (both) Geometry
4583 (both) Introduction to Mathematical Modeling
4663 (both) Combinatorial Mathematics.
4713 (both) Number Theory
CIED 4003 (MM only) Teaching Fundamental Concepts of Mathematics.
CIED 4053 (MM only) Teaching Geometry in the Secondary School
STAT 4013 or 4023 (both) Statistical Methods I or II
CS 1103 or 1113 (SE only) Computer Programming or Computer Science I
12 hours from below(MM) / 3 hours from bolded courses below and/or 4023 (above) (SE):
4013 Calculus of Several Variables
4143 Advanced Calculus I
4153 Advanced Calculus II
4233 Intermediate Differential Equations
4263 Introduction to Partial Differential Equations
4283 Complex Variables
4453 Mathematical Interest Theory
4513 Numerical Mathematics: Analysis
4553 Linear and Nonlinear Programming
4583 Introduction to Mathematical Modeling
4613 Modern Algebra I
4623 Modern Algebra II
4713 Number Theory
4813 Groups and Representations
5023 Advanced Linear Algebra
5213 Fourier Analysis and Wavelets
5303 General Topology
5593 Methods of Applied Mathematics
6 hours of MATH or STAT (4000 or above) or upper-division CS or PHYS (MM only)
